I present arguments against both explicit and implicit versions of the simulation theory for intersubjective understanding. Logical, developmental, and phenomenological evidence counts against the concept of explicit simulation if this is to be understood as the pervasive or default way that we understand others. The concept of implicit (subpersonal) simulation, identified with neural resonance systems (mirror systems or shared representations), fails to be the kind of simulation required by simulation theory, because it fails to explain how neuronal processes meet constraints that involve instrumentality and pretense. Implicit simulation theory also fails to explain how I can attribute a mental or emotion state that is different from my own to another person. I also provide a brief indication of an alternative interpretation of neural resonance systems.